Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditional optimal mechanism design approach is ill-suited --- either because it makes overly strong assumptions, or because it advocates overly complex designs. The thesis of this paper is that approximately optimal mechanisms allow us to reason about fundamental questions that seem out of reach of the traditional theory. This survey has three main parts. The first part describes the approximately optimal mechanism design paradigm --- how it works, and what we aim to learn by applying it. The second and third parts of the survey cover two case studies, where we instantiate the general design paradigm to investigate two basic questions. In the first example, we consider revenue maximization in a single-item auction with heterogeneous bidders. Our goal is to understand if complexity --- in the sense of detailed distributional knowledge --- is an essential feature of good auctions for this problem, or alternatively if there are simpler auctions that are near-optimal. The second example considers welfare maximization with multiple items. Our goal here is similar in spirit: when is complexity --- in the form of high-dimensional bid spaces --- an essential feature of every auction that guarantees reasonable welfare? Are there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on Economics and Computation (EC), June 201

A Novel Method to Calculate Click Through Rate for Sponsored Search

Sponsored search adopts generalized second price (GSP) auction mechanism which works on the concept of pay per click which is most commonly used for the allocation of slots in the searched page. Two main aspects associated with GSP are the bidding amount and the click through rate (CTR). The CTR learning algorithms currently being used works on the basic principle of (#clicks_i/ #impressions_i) under a fixed window of clicks or impressions or time. CTR are prone to fraudulent clicks, resulting in sudden increase of CTR. The current algorithms are unable to find the solutions to stop this, although with the use of machine learning algorithms it can be detected that fraudulent clicks are being generated. In our paper, we have used the concept of relative ranking which works on the basic principle of (#clicks_i /#clicks_t). In this algorithm, both the numerator and the denominator are linked. As #clicks_t is higher than previous algorithms and is linked to the #clicks_i, the small change in the clicks which occurs in the normal scenario have a very small change in the result but in case of fraudulent clicks the number of clicks increases or decreases rapidly which will add up with the normal clicks to increase the denominator, thereby decreasing the CTR.Comment: 10 pages, 1 figur

Characterizing Optimal Adword Auctions

We present a number of models for the adword auctions used for pricing advertising slots on search engines such as Google, Yahoo! etc. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for this auction with a multi-dimensional type-space that are {\em not} affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity $O(n^2m^2)$ and $O(n^2m^3)$ respectively, where $n$ is number of bidders and $m$ is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The numerical results suggest that customized rank-based allocation rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c) Decision Sciences Seminar, Fuqua School of Business, Duke Universit